How the built environment affects urban vitality at the block scale: Empirical evidence from Xi’an’s central urban area

The built environment is critical in fostering vibrant cities, and evaluating urban vitality (UV) and its interplay with the built environment is essential for building people-oriented cities. Most existing studies have overlooked the nonlinear relationship, threshold effects, and spatial heterogeneity of the built environment on UV. Taking the Xi’an central urban area as a case study, this study constructs a block-scale UV evaluation index system and a built environment indicator system based on multi-source data. Then, the nonlinear effects of built environment factors on UV are explored via the Geographically Weighted Random Forest (GWRF) and SHapley Additive exPlanations (SHAP) models. The findings show that the spatial distribution of UV exhibits a core-periphery structure and transportation dependence characteristics. Among various built environment factors, floor area ratio (FAR) and mixed land use (MLU) are identified as key drivers. UV exhibits an S-shaped curve with FAR and diminishing returns with MLU. Spatial heterogeneity indicates that the polycentric UV spatial pattern as a pivotal model for improving urban quality and efficiency stage. This study provides empirical foundations for the refined governance and high-quality development of UV.